The time it takes a home building company to build a new home is directly proportional to the size of the home and inversely proportional to the number of people on the building crew. If it takes 10 workers 4 weeks to build a 2,000 square foot home, how long will it take 6 workers to build the home?
Let t = time it takes to build a home
w = number of workers
s = size of home
The joint variation between these variables can be represented by
t = ks/w
Substitute 4 for t, 2000 for s and 10 for w and solve for k.
4 = k(2000)/10
Multiply both sides by 10 to clear the denominator.
40 = k(2000)
Divide by 2000 to get
40/2000 = 1/50 = k.
Now substitute 6 for w, 2000 for s and 1/50 for k and solve for t.
t = (1/50)(2000/6)
t = 2000/300, t = 6.66. Therefore, it takes 6 workers 6 2/3 weeks to build a 2,000 square foot home.